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Coherence transformations in single qubit systems

We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence-preserving operation (CPO). Quantitative connection has been built between IO...

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Autores principales: Shi, Hai-Long, Wang, Xiao-Hui, Liu, Si-Yuan, Yang, Wen-Li, Yang, Zhan-Ying, Fan, Heng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5666013/
https://www.ncbi.nlm.nih.gov/pubmed/29093505
http://dx.doi.org/10.1038/s41598-017-13687-4
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author Shi, Hai-Long
Wang, Xiao-Hui
Liu, Si-Yuan
Yang, Wen-Li
Yang, Zhan-Ying
Fan, Heng
author_facet Shi, Hai-Long
Wang, Xiao-Hui
Liu, Si-Yuan
Yang, Wen-Li
Yang, Zhan-Ying
Fan, Heng
author_sort Shi, Hai-Long
collection PubMed
description We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence-preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO ⊂ PIO ⊂ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations.
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spelling pubmed-56660132017-11-08 Coherence transformations in single qubit systems Shi, Hai-Long Wang, Xiao-Hui Liu, Si-Yuan Yang, Wen-Li Yang, Zhan-Ying Fan, Heng Sci Rep Article We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence-preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO ⊂ PIO ⊂ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations. Nature Publishing Group UK 2017-11-01 /pmc/articles/PMC5666013/ /pubmed/29093505 http://dx.doi.org/10.1038/s41598-017-13687-4 Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Shi, Hai-Long
Wang, Xiao-Hui
Liu, Si-Yuan
Yang, Wen-Li
Yang, Zhan-Ying
Fan, Heng
Coherence transformations in single qubit systems
title Coherence transformations in single qubit systems
title_full Coherence transformations in single qubit systems
title_fullStr Coherence transformations in single qubit systems
title_full_unstemmed Coherence transformations in single qubit systems
title_short Coherence transformations in single qubit systems
title_sort coherence transformations in single qubit systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5666013/
https://www.ncbi.nlm.nih.gov/pubmed/29093505
http://dx.doi.org/10.1038/s41598-017-13687-4
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